Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}8x-2y &= 8 \\ x+y &= 2\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {-x+2}$ Substitute this expression for $y$ in the first equation. $8x-2({-x + 2}) = 8$ $8x + 2x - 4 = 8$ Simplify by combining terms, then solve for $x$ $10x - 4 = 8$ $10x = 12$ $x = \dfrac{6}{5}$ Substitute $\dfrac{6}{5}$ for $x$ back into the top equation. $8( \dfrac{6}{5})-2y = 8$ $\dfrac{48}{5}-2y = 8$ $-2y = -\dfrac{8}{5}$ $y = \dfrac{4}{5}$ The solution is $\enspace x = \dfrac{6}{5}, \enspace y = \dfrac{4}{5}$.